1. McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 1 An Introduction to Business Statistics

2. 1-2 An Introduction to Business Statistics 1.1Populations and SamplesPopulations and Samples 1.2Sampling a Population of Existing UnitsSampling a Population of Existing Units 1.3Sampling a ProcessSampling a Process 1.4Ratio, Interval, Ordinal, and Nominative Scales of Measurement (Optional)Ratio, Interval, Ordinal, and Nominative Scales of Measurement 1.5 An introduction to survey sampling (Optional)An introduction to survey sampling

3. 1-3 Populations and Samples PopulationA set of existing units (people, objects, or events) VariableA measurable characteristic of the population CensusAn examination of the entire population of measurements SampleA selected subset of the units of a population

4. 1-4 Terminology 1 Measurement The process of measuring to find out the extent, quantity, amount, and so on, of the variable of interest for some item from the population Produces data For example, collecting annual starting salaries of graduates from last year’s MBA program Value The result of measurement The specific measurement for a particular unit in the population For example, the starting salaries of graduates from last year’s MBA Program

5. 1-5 Terminology 2 Quantitative Measurements that represent quantities (for example, “how much” or “how many”) Annual starting salary is quantitative Age and number of children is also quantitative Qualitative A descriptive category to which a population unit belongs. Also, a descriptive attribute of a population unit A person’s gender is qualitative So is their hair color

6. 1-6 Terminology 3 Population of measurements Measurement of the variable of interest for each and every population unit Sometimes referred to as an observation For example, annual starting salaries of all graduates from last year’s MBA program The process of collecting the population of all measurements is a census Census usually too expensive, too time consuming, and too much effort for a large population

7. 1-7 Terminology 4 Sample A subset of population units For example, a university graduated 8,742 students This is too large for a census So, we select a sample of these graduates and learn their annual starting salaries Sample of measurements Measured values of the variable of interest for the sample units For example, the actual annual starting salaries of the sampled graduates

8. 1-8 Terminology 5 Descriptive statistics The science of describing the important aspects of a set of measurements For example, for a set of annual starting salaries, want to know: How much to expect What is a high versus low salary How much the salaries differ from each other If the population is small enough, could take a census and not have to sample and make any statistical inferences But if the population is too large, then …

9. 1-9 Terminology 6 Statistical Inference The science of using a sample of measurements to make generalizations about the important aspects of a population of measurements For example, use a sample of starting salaries to estimate the important aspects of the population of starting salaries

10. 1-10 Sampling a Population of Existing Units Random sample A random sample is a sample selected from a population so that: Each population unit has the same chance of being selected as every other unit Each possible sample (of the same size) has the same chance of being selected For example, randomly pick two different people from a group of 15: Number the people from 1 to 15; and write their numbers on 15 different slips of paper Thoroughly mix the papers and randomly pick two of them The numbers on the slips identifies the people for the sample

11. 1-11 How to Pick? Sample with replacement Replace each sampled unit before picking next unit The unit is placed back into the population for possible reselection However, the same unit in the sample does not contribute new information Sample without replacement A sampled unit is withheld from possibly being selected again in the same sample Guarantees a sample of different units Each sampled unit contributes different information Sampling without replacement is the usual and customary sampling method

12. 1-12 Approximately Random Samples In general, must make a list identifying each and every individual population unit (called a frame) If the population is very large, it may not be possible to list every individual population unit So instead draw a “systematic” sample Randomly enter the population and systematically sample every k th unit This usually approximates a random sample Read Example 1.2, “Marketing Research Case: Rating a New Bottle Design,” in the textbook

13. 1-13 Another Sampling Method Voluntary response sample Participants select themselves to be in the sample Participants “self-select” For example, calling in to vote on American Idol Commonly referred to as a “non-scientific” sample Usually not representative of the population Over-represent individuals with strong opinions Usually, but not always, negative opinions

14. 1-14 Process A sequence of operations that takes inputs (labor, raw materials, methods, machines, and so on) and turns them into outputs (products, services, and the like) Process Inputs Outputs Sampling a Process

15. 1-15 Process “Population” The “population” from a process is all output produced in the past, present, and the yet-to-occur future For example, all automobiles of a particular make and model, for instance, the Lincoln Town Car Cars will continue to be made over time

16. 1-16 Population Size A population may be “finite” or “infinite” Finite if it is of fixed and limited size Finite if it can be counted Even if very large For example, all the Lincoln Town Cars actually made during just this model year is a finite population Because a specific number of cars was made between the start and end of the model year Infinite if it is unlimited Infinite if listing or counting every element is impossible For example, all the Lincoln Town Car’s that could have possibly been made this model year is an infinite population

17. 1-17 Statistical Control A process is in statistical control if it does not exhibit any unusual process variations A process in statistical control displays a constant amount of variation around a constant level A process not in statistical control is “out of control” To determine if a process is in control or not, sample the process often enough to detect unusual variations Issue: How often to sample? See Example 1.3, “The Coffee Temperature Case: Monitoring Coffee Temperature” in the textbook

18. 1-18 A runs plot is a graph of individual process measurements over time Runs Plot

19. 1-19 Statistical Process Control The real purpose is to see if the process is out of control so that corrective action can be taken if necessary Must investigate further to find out why the process is going out of control See Example 1.4, The Car Mileage Case: Estimating Mileage More on statistical process control in Chapter 14

20. 1-20 Scales of Measurement Qualitative variables Descriptive categorization of population or sample units Two types: Nominative Ordinal Quantitative variables Numerical values represent quantities measured with a fixed or standard unit of measure Two types: Interval Ratio

21. 1-21 Qualitative Variables Nominative: Identifier or name Unranked categorization Example: gender, car color Ordinal: All characteristics of nominative plus… Rank-order categories Ranks are relative to each other Example: Low (1), moderate (2), or high (3) risk

22. 1-22 Interval Variable All of the characteristics of ordinal plus… Measurements are on a numerical scale with an arbitrary zero point The “zero” is assigned: it is unphysical and not meaningful Zero does not mean the absence of the quantity that we are trying to measure Can only meaningfully compare values in terms of the interval between them Cannot compare values by taking their ratios “Interval” is the arithmetic difference between the values Example: temperature 0  F means “cold,” not “no heat” 80  F is NOT twice as warm as 40  F But 80  F is 40  warmer than 40  F

23. 1-23 Ratio Variable All the characteristics of interval plus… Measurements are on a numerical scale with a meaningful zero point Zero means “none” or “nothing” Values can be compared in terms of their interval and ratio $30 is $20 more than $10 $30 is 3 times as much as $10 $0 means no money In business and finance, most quantitative variables are ratio variables, such as anything to do with money Examples: Earnings, profit, loss, age, distance, height, weight

24. 1-24 Survey Sampling Already know some sampling methods Also called sampling designs, they are: Random sampling The focus of this book Systematic sampling Voluntary response sampling But there are other sample designs: Stratified random sampling Cluster sampling

25. 1-25 Stratified Random Sample Divide the population into non-overlapping groups, called strata, of similar units Separately, select a random sample from each and every stratum Combine the random samples from each stratum to make the full sample Appropriate when the population consists of two or more different groups so that: The groups differ from each other with respect to the variable of interest Units within a group are similar to each other For example, divide population into strata by age, gender, income, etc

26. 1-26 Cluster Sampling “Cluster” or group a population into subpopulations Cluster by geography, time, and so on… Each cluster is a representative small-scale version of the population (i.e. heterogeneous group) A simple random sample is chosen from each cluster Combine the random samples from each cluster to make the full sample Appropriate for populations spread over a large geographic area so that… There are different sections or regions in the area with respect to the variable of interest A random sample of the cluster

27. 1-27 Sampling Problems Random sampling should eliminate bias But even a random sample may not be representative because of: Under-coverage Too few sampled units or some of the population was excluded Non-response When a sampled unit cannot be contacted or refuses to participate Response bias Responses of selected units are not truthful